Numerical solution of the schrödinger equation with periodic coulomb potential

This paper investigates the energy spectrum of a periodic one-dimensional Coulomb potential. The Schrödinger equation is solved numerically by our newly developed filter method (Phys. Rev E 96(3), 033302 (2017)). We observe that the energy spectrum can be obtained with a limited number of lattice. The results show the presence of an energy band structure as a function of lattice width and edge width. The comparison with the other potential model is also discussed.